ON SOME CLASSES OF THE WEAKLY SUBDIFFERENTIAL FUNCTIONS

Yıl 2025, Cilt: 13 Sayı: 1, 24 - 34, 28.02.2025

Samet Bila , Refail Kasımbeyli

Öz

This work presents a theorem that any Lipschitz function is weakly subdifferentiable with x^* component of the weak subgradient is different from 0_(R^n ). This theorem is based on Kasimbeyli's nonlinear cone separation theorem. Also, we show that any positively homogeneous and continuous function is both upper and lower Lipschitz. Additionally, we show that positively homogeneous and lower semicontinuous functions are weakly subdifferentiable that the pair (x^*,c) which is a weak subgradient of a function in this case is different from (0_(R^n ),0).

Anahtar Kelimeler

Nonconvex Optimization, The Weak Subdifferential, Lipschitz functions, Operations Research

ON SOME CLASSES OF WEAKLY SUBDIFFERENTIABLE FUNCTIONS

Öz

This work presents a theorem that any Lipschitz function is weakly subdifferentiable with x^* component of the weak subgradient is different from 0_(R^n ). This theorem is based on Kasimbeyli's nonlinear cone separation theorem. Also, we show that any positively homogeneous and continuous function is both upper and lower Lipschitz. Additionally, we show that positively homogeneous and lower semicontinuous functions are weakly subdifferentiable that the pair (x^*,c) which is a weak subgradient of a function in this case is different from (0_(R^n ),0).

Anahtar Kelimeler

Nonconvex Optimization, The Weak Subdifferential, Lipschitz functions, Operations Research

Kaynakça

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